Average Error: 14.5 → 0.1
Time: 12.0s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{-1}{1 + x}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{-1}{1 + x}}{x}
double f(double x) {
        double r3322686 = 1.0;
        double r3322687 = x;
        double r3322688 = r3322687 + r3322686;
        double r3322689 = r3322686 / r3322688;
        double r3322690 = r3322686 / r3322687;
        double r3322691 = r3322689 - r3322690;
        return r3322691;
}
↓
double f(double x) {
        double r3322692 = 1.0;
        double r3322693 = -r3322692;
        double r3322694 = x;
        double r3322695 = r3322692 + r3322694;
        double r3322696 = r3322693 / r3322695;
        double r3322697 = r3322696 / r3322694;
        return r3322697;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.5

    \[\frac{1}{x + 1} - \frac{1}{x}\]
  2. Using strategy rm

  3. Applied frac-sub13.9

    \[\leadsto \color{blue}{\frac{1 \cdot x - \left(x + 1\right) \cdot 1}{\left(x + 1\right) \cdot x}}\]

  4. Taylor expanded around 0 0.4

    \[\leadsto \frac{\color{blue}{-1}}{\left(x + 1\right) \cdot x}\]
  5. Using strategy rm

  6. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{-1}{x + 1}}{x}}\]

  7. Final simplification0.1

    \[\leadsto \frac{\frac{-1}{1 + x}}{x}\]

Reproduce

herbie shell --seed 2019169 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))